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- W2002183561 abstract "We explore the extent to which a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with the Schrödinger operator on a half-line to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation, generalizes to higher dimensions. In this multi-dimensional extension the half-line is replaced by an open set Ω⊂Rn, n∈N, n⩾2, where Ω has a compact, nonempty boundary ∂Ω satisfying certain regularity conditions. Our variant involves ratios of perturbation determinants corresponding to Dirichlet and Neumann boundary conditions on ∂Ω and invokes the corresponding Dirichlet-to-Neumann map. As a result, we succeed in reducing a certain ratio of modified Fredholm perturbation determinants associated with operators in L2(Ω;dnx), n∈N, to modified Fredholm determinants associated with operators in L2(∂Ω;dn−1σ), n⩾2. Applications involving the Birman–Schwinger principle and eigenvalue counting functions are discussed." @default.
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- W2002183561 date "2007-12-01" @default.
- W2002183561 modified "2023-10-16" @default.
- W2002183561 title "Variations on a theme of Jost and Pais" @default.
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- W2002183561 doi "https://doi.org/10.1016/j.jfa.2007.05.009" @default.
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